146 



onl}' for lower temperatures. And this shows at the same time the 

 incorrectness of the extrapolation carried out by Smits. 



At all temperatures, liowever, van der Waals' vajiour pressure 

 holds, which may be written in the form : 



log P = if + log pk) ^, (a) 



in which ƒ is still a temperature function. When we compare this 

 expression with the integrated formula d log p = etc., on the assump- 

 tion of ?. = ;.„ — q RT, i. e. with 



logp—C———(iloglz=C , . {h) 



it appears that in the formula used by Smits, which — we repeat 

 it — holds only for relatively low values, the constant C will be 

 = /o + % Vk, and that l^=f^RTjc. But though the foiin of the 

 last formula shows resemblance with Van der Waals' formula, the 

 numerator of the term with Vr will be in no connection at all 

 with X at higher temperatures, as X will approach at Tk, while 

 the numerator mentioned reaiains finite, and is virtually =f7\, accord- 

 ing to Van der Waals' formula. 



2. On the assumption of the quadratic relation 

 t = tk — « h i^ 



^k -ik 



for the portion of the vapour pressure curve between the minimum 

 and the critical temperature, I calculated the values « = 11,71, 

 ^ = 26,62, fj. = 3,77 , p^ = 95,3 for the four unknown quantities 

 «, (5, fk, and pk from the four vapour pressure observations at 504°, 

 550°, 593°, and 634°. 



However — neither the values T/t=: 968,1, />i = 95, nor even 

 with the somewhat lower pressure 90 atm., can satisfy us. It is 

 namely almost sure that at 695° C, according to the determinations 

 of the density of Stock, Gibson and Stamm (J 912), the phosphorus 

 vapour is still quite normal, i.e. = P^, even at the low pressure of 

 75 m.m. And this will a fortiori be the case at a pressure of 80 

 a 90 atm. (i.e. at a total pressure, internal and external pressure 

 combined, of fk X 80 or 90 = ± 640 or 720 atm.). The same thing 

 follows also from Preuner and Brockmöller's determinations (Z. f. 

 ph. Chem. 81, p. 159 (1912)). 



From the formula hk^ RTk:Spk the value 465. JO" ^ would now 

 follow for 6a,- with 7;. = 968,1, /9;t = 95,3 ; and with />t = 90 the 

 value 492. 10-5. Both most probably too low, as 4 X 140 = 560.10-5 

 may be expected. 



